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2 ENGINE PERFORMANCE
2.1 METHOD OF CALCULATING THE THRUST FORCES
The thrust forces or gas loads can be calculated for the engine, or for any flow
section of the engine, provided that the areas, pressures, velocities and mass flow
are known for both the inlet and outlet of the particular flow section.
The distribution of thrust forces shown in Fig 2.1. can be calculated by considering
each component in turn and applying some simple calculations. The thrust produced
by the engine is mainly the product of the mass of air passing through the engine and
the velocity increase imparted to it (ie. Newtons Second Law of Motion), however the
pressure difference between the inlet to and the outlet from the particular flow section
will have an effect on the overall thrust of the engine and must be included in the
calculation.

FORWARD GAS LOAD 57836 lbs REARWARD GAS LOAD 46678 lbs
TOTAL THRUST 11158 lbs

Thrust Distribution of a Typical Single Spool Axial Flow Engine.

Figure 2.1.
To calculate the resultant thrust for a particular flow section it is necessary to
calculate the total thrust at both inlet and outlet, the resultant thrust being the
difference between the two values obtained.

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Calculation of the thrust is achieved using the following formula:

WvJ
Thrust = ( A × P) +
g
Where A = Area of flow section in sq. in.
P = Pressure in lb. per sq. in.
W = Mass flow in lb. per sec.
VJ = Velocity of flow in feet per sec.
g = Gravitational constant 32.2 ft. per sec. per sec.
2.2 CALCULATING THE THRUST OF THE ENGINE
When applying the above method to calculate the individual thrust loads on the
various components it is assumed that the engine is static. The effect of aircraft
forward speed on the engine thrust will be dealt with later. In the following
calculations ‘g’ is taken to be 32 for convenience.
2.2.1. Compressor casing
To obtain the thrust on the compressor casing, it is necessary to calculate the
conditions at the inlet to the compressor and the conditions at the outlet from the
compressor. Since the pressure and the velocity at the inlet to the compressor are
zero, it is only necessary to consider the force at the outlet from the compressor.
Therefore, given that the compressor –
OUTLET Area (A) = 182 sq. in.
Pressure (P) = 94 lb. per sq. in. (gauge)
Velocity (vj) = 406 ft. per sec.
Mass flow (W) = 153 lb. per sec.
The thrust
Wv j
= ( A × P) + −0
g
153 × 406
= (182 × 94) + −0
32
= 19,049lb. of thrust in a forward direction.

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Total Thrust of the Compressor.

Figure 2.2.

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International Standard Atmosphere

Figure 2.3.

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2.2.1 CHOKED NOZZLE

Considering the formula for thrust under “choked” nozzle conditions:
Wv J
Thrust = ( P − P0 )A +
g
Where: P = Pressure
P = Ambient Pressure
A = Area
W = Mass Flow
V = Velocity
It can be seen that the thrust can be further affected by a change in the mass flow
rate of air through the engine and by a change in jet velocity. An increase in mass
airflow may be obtained by using water injection to cool the air and increases in jet
velocity by using after-burning.
Changes in ambient pressure and temperature considerably influence the thrust of
the engine. This is because of the way they affect the air density and hence the
mass of air entering the engine for a given engine rotational speed.
Thrust Correction - Turbojet
To enable the performance of similar engines to be compared when operating under
different climatic conditions, or at different altitudes, correction factors must be
applied to the calculations to return the observed values to those which would be
found under I.S.A. conditions. For example, the thrust correction for a turbo-jet
engine is:
30
Thrust (lb) (corrected) = thrust (lb) (observed) x
PO
• Where P0 = atmospheric pressure in inches of mercury (in Hg)
(observed)
30 = I.S.A. standard sea level pressure (in Hg)
Shaft Horsepower Correction - Turboprop
The observed performance of the turbo-propeller engine is also corrected to I.S.A.
conditions, but due to the rating being in s.h.p. and not in pounds of thrust the factors
are different. For example, the correction for s.h.p. is:
30 273 + 15
S.h.p. (corrected) = s.h.p. (observed) × ×
PO 273 + TO
Where P0 = atmospheric pressure (in Hg) (observed)
T0 = atmospheric temperature in deg. C (observed)
30 = I.S.A. standard sea level pressure (in Hg)
273 + 15 = I.S.A. standard sea level temperature in deg. K
273 + T0 = Atmospheric temperature in deg. K

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Equivalent Shaft Horsepower (EHP)

In practice there is always a certain amount of jet thrust in the total output of the
turbo-propeller engine and this must be added to the s.h.p. The correction for jet
thrust is the same as that specified earlier.
To distinguish between these two aspects of the power output, it is usual to refer to
them as s.h.p. and thrust horse-power (t.h.p.). The total equivalent horsepower is
denoted by t.e.h.p. (sometimes e.h.p.) and is the s.h.p. plus the s.h.p. equivalent to
the net jet thrust. For estimation purposes it is taken that, under sea-level static
conditions, one s.h.p. is equivalent to approximately 2.6 lb. of jet thrust. Therefore:
jet thrust lb.
t.e.h.p. = s.h.p. +
2.6
The ratio of jet thrust to shaft power is influenced by many factors. For instance, the
higher the aircraft operating speed the larger may be the required proportion of total
output in the form of jet thrust. Alternatively, an extra turbine stage may be required
if more than a certain proportion of the total power is to be provided at the shaft. In
general, turbo-propeller aircraft provide one pound of thrust for every 3.5 h.p. to 5
h.p.
2.2.2 COMPARISON BETWEEN THRUST AND HORSE-POWER
Because the turbo-jet engine is rated in thrust and the turbo-propeller engine in
s.h.p., no direct comparison between the two can be made without a power
conversion factor. However, since the turbo-propeller engine receives its thrust
mainly from the propeller, a comparison can be made by converting the horse-power
developed by the engine to thrust or the thrust developed by the turbo-jet engine to
t.h.p.; that is, by converting work to force or force to work. For this purpose, it is
necessary to take into account the speed of the aircraft.
FV
t.h.p. is expressed as
550 ft . per sec
Where F = lb. of thrust
V = aircraft speed (ft. per sec)

Since one horse-power is equal to 550 ft.lb. per sec. and 550 ft. per sec. is equivalent
to 375 miles per hour, it can be seen from the above formula that one lb. of thrust
equals one t.h.p. at 375 m.p.h. It is also common to quote the speed in knots
(nautical miles per hour); one knot is equal to 1.1515 m.p.h. or one pound of thrust is
equal to one t.h.p. at 325 knots.
Thus if a turbo-jet engine produces 5,000 lb. of net thrust at an aircraft speed of 600
5 , 000 × 600
m.p.h. the t.h.p. would be = 8 , 000
375

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However, if the same thrust was being produced by a turbo-propeller engine with a
propeller efficiency of 55 percent at the same flight speed of 600 m.p.h., then the
100
t.h.p. would be: 8,000 × = 14,545
55
Thus at 600 m.p.h. one lb. of thrust is the equivalent of about 3 t.h.p.
2.3 ENGINE THRUST IN FLIGHT
Since reference will be made to gross thrust, momentum drag and net thrust, it will
be helpful to define these terms:
Gross or total thrust is the product of the mass of air passing through the engine and
the jet velocity at the propelling nozzle, expressed as:
Wv J
( P − P0 )A +
g
The momentum drag is the drag due to the momentum of the air passing into the
WV
engine relative to the aircraft velocity, expressed as where:
g
W = Mass flow in lb. per sec.
V = Velocity of aircraft in feet per sec.
G = Gravitational constant 32.2 ft. per sec. per sec.
 WVJ
 ⇐ Momentum Thrust =
WV wv  g
Momentum Drag = ⇒⇐ Gross Thrust = ( P − Po ) A + J 
g g  ⇐ Pr essure Thrust = ( P − PO ) A


The Balance of Forces and Expression for Thrust and Momentum Drag
Figure 2.4.
(Figure 2.4. refers)The net thrust or resultant force acting on the aircraft in flight is the
difference between the gross thrust and the momentum drag. From the definitions
and formulae stated earlier under flight conditions, the net thrust of the engine,
W (Vj − V )
simplifying, can be expressed as: (P − Po ) A +
g
All pressures are total pressures except P, which is static pressure at the propelling
nozzle

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W= Mass of air passing through engine (lb. Per sec.)

VJ = Jet velocity at propelling nozzle (ft. per sec)
P = Static pressure across propelling nozzle (lb. Per sq. in)
PO = Atmospheric pressure (lb. Per sq. in)
A = Propelling nozzle area (sq. in)
V = Aircraft speed (ft. per sec.)
G = Gravitational constant 32.2

Graph of Thrust Against Forward Speed.

Figure 2.5.

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2.3.1 EFFECT OF FORWARD SPEED

Since reference will be made to ‘ram ratio’ and Mach number, these terms are
defined as follows:
Ram ratio is the ratio of the total air pressure at the engine compressor entry to the
static air pressure at the air intake entry.
Mach number is an additional means of measuring speed and is defined as the ratio
of the speed of a body to the local speed of sound. Mach 1.0 therefore represents a
speed equal to the local speed of sound.
From the thrust equation, it is apparent that if the jet velocity remains constant,
independent of aircraft speed, then as the aircraft speed increases the thrust would
decrease in direct proportion. However, due to the ‘ram ratio’ effect from the aircraft
forward speed, extra air is taken into the engine so that the mass airflow and also the
jet velocity increase with aircraft speed. The effect of this tends to offset the extra
intake momentum drag due to the forward speed so that the resultant loss of net
thrust is partially recovered as the aircraft speed increases. A typical curve
illustrating this point is shown in the figure 2.5. Obviously, the ‘ram ratio’ effect, or the
return obtained in terms of pressure rise at entry to the compressor in exchange for
the unavoidable intake drag, is of considerable importance to the turbo-jet engine,
especially at high speeds. Above speeds of Mach 1.0, as a result of the formation of
shock waves at the air intake, this rate of pressure rise will rapidly decrease unless a
suitably designed air intake is provided; an efficient air intake is necessary to obtain
maximum benefit from the ram ratio effect.
As aircraft speeds increase into the supersonic region, the ram air temperature rises
rapidly consistent with the basic gas laws. This temperature rise affects the
compressor delivery air temperature proportionally and, in consequence, to maintain
the required thrust, the engine must be subjected to higher turbine entry
temperatures. Since the maximum permissible turbine entry temperature is
determined by the temperature limitations of the turbine assembly, the choice of
turbine materials and the design of blades and stators to permit cooling are very
important.
With an increase in forward speed, the increased mass airflow due to the ‘ram ratio’
effect must be matched by the fuel flow and the result is an increase in fuel
consumption. Because the net thrust tends to decrease with forward speed, the end
result is an increase in specific fuel consumption (s.f.c.), as shown by the curves for a
typical turbo-jet engine in the figure 2.6.
At high forward speeds at low altitudes, the ‘ram ratio’ effect causes very high
stresses on the engine and, to prevent over-stressing, the fuel flow is automatically
reduced to limit the engine speed and airflow.

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Effects of speed on Thrust and Fuel Consumption.

Figure 2.6.

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2.3.2 EFFECT OF AFTERBURNING ON ENGINE THRUST

At take-off conditions, the momentum drag of the airflow through the engine is
negligible, so that the gross thrust can be considered to be equal to the net thrust. If
after-burning is selected, an increase in take-off thrust in the order of 30 percent is
possible with the pure jet engine and considerably more with the by-pass engine.
This augmentation of basic thrust, is of greater advantage for certain specific
operating requirements.
Under flight conditions, however, this advantage is even greater, since the
momentum drag is the same with or without after-burning and, due to the ram effect,
better utilisation is made of every pound of air flowing through the engine.
2.3.3 EFFECT OF ALTITUDE
With increasing altitude the ambient air pressure and temperature are reduced. This
affects the engine in two inter-related ways:-
The fall of pressure reduces the air density and hence the mass airflow into the
engine for a given engine speed. This causes the thrust or s.h.p. to fall. The fuel
control system adjusts the fuel pump output to match the reduced mass airflow, so
maintaining a constant engine speed.
The fall in air temperature increases the density of the air, so that the mass of air
entering the compressor for a given engine speed is greater. This causes the mass
airflow to reduce at a lower rate and so compensates to some extent for the loss of
thrust due to the fall in atmospheric pressure. At altitudes above 36,089 feet and up
to 65,617 feet, however, the temperature remains constant, and the thrust or s.h.p. is
affected by pressure only.
Graphs showing the typical effect of altitude on thrust and fuel consumption are
illustrated in Figure 2.7.

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Effects of Altitude on Thrust and Fuel Consumption.

Figure 2.7.

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2.3.4 EFFECT OF TEMPERATURE

On a cold day the density of the air increases so that the mass of air entering the
compressor for a given engine speed is greater, hence the thrust or s.h.p. is higher.
The denser air does, however, increase the power required to drive the compressor
or compressors; thus the engine will require more fuel to maintain the same engine
speed or will run at a reduced engine speed if no increase in fuel is available.
On a hot day the density of the air decreases, thus reducing the mass of air entering
the compressor and, consequently, the thrust of the engine for a given r.p.m.
Because less power will be required to drive the compressor, the fuel control system
reduces the fuel flow to maintain a constant engine rotational speed or turbine entry
temperature, as appropriate; however, because of the decrease in air density, the
thrust will be lower. At a temperature of 45°C, depending on the type of engine, a
thrust loss of up to 20 percent may be experienced. This means that some sort of
thrust augmentation, such as water injection, may be required.
The fuel control system, controls the fuel flow so that the maximum fuel supply is
held practically constant at low air temperature conditions, whereupon the engine
speed falls but, because of the increased mass airflow as a result of the increase in
air density, the thrust remains the same. For example, the combined acceleration
and speed control (CASC) fuel system schedules fuel flow to maintain a constant
engine r.p.m., hence thrust increases as air temperature decreases until, at a
predetermined compressor delivery pressure, the fuel flow is automatically controlled
to maintain a constant compressor delivery pressure and, therefore, thrust, Figure
2.8. illustrates this for a twin-spool engine where the controlled engine r.p.m. is high
pressure compressor speed and the compressor delivery pressure is expressed as
P3. It will also be apparent from this graph that the low pressure compressor speed
is always less than its limiting maximum and that the difference in the two speeds is
reduced by a decrease in ambient air temperature. To prevent the L.P. compressor
overspeeding, fuel flow is also controlled by an L.P. governor which, in this case,
takes a passive role.

The Effect of Air

Temperature on
a Typical Twin
Spool Engine
Figure 2.8.

2.4 PROPULSIVE EFFICIENCY

Performance of the jet engine is not only concerned with the thrust produced, but
also with the efficient conversion of the heat energy of the fuel into kinetic energy, as

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represented by the jet velocity, and the best use of this velocity to propel the aircraft
forward, ie. the efficiency of the propulsive system.
The efficiency of conversion of fuel energy to kinetic energy is termed thermal or
internal efficiency and, like all heat engines, is controlled by the cycle pressure ratio
and combustion temperature. Unfortunately this temperature is limited by the
thermal and mechanical stresses that can be tolerated by the turbine. The
development of new materials and techniques to minimise these limitations is
continually being pursued.
The efficiency of conversion of kinetic energy to propulsive work is termed the
propulsive or external efficiency and this is affected by the amount of kinetic energy
wasted by the propelling mechanism. Waste energy dissipated in the jet wake, which
represents a loss, can be expressed as
W (v j − V ) 2
where (vJ - V) is the waste velocity.
2g
It is therefore apparent that at the aircraft lower speed range the pure jet stream
wastes considerably more energy than a propeller system and consequently is less
efficient over this range. However, this factor changes as aircraft speed increases,
because although the jet stream continues to issue at a high velocity from the engine,
its velocity relative to the surrounding atmosphere is reduced and, in consequence,
the waste energy loss is reduced.

Efficiency Plots of Differing Types of Engine to Airspeed

Figure 2.9.
2.5 FUEL CONSUMPTION AND POWER TO WEIGHT RELATIONSHIP
Primary engine design considerations, particularly for commercial transport duty, are
those of low specific fuel consumption and weight. Considerable improvement has
been achieved by use of the by-pass principle and by advanced mechanical and

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aerodynamic features and the use of improved materials. With the trend towards
higher by-pass ratios, in the range of 15:1, the triple-spool and contra-rotating rear
fan engines allow the pressure and by-pass ratios to be achieved with short rotors,
using fewer compressor stages, resulting in a lighter and more compact engine.
S.f.c. is directly related to the thermal and propulsive efficiencies; that is, the overall
efficiency of the engine. Theoretically, high thermal efficiency requires high
pressures which in practice also means high turbine entry temperatures. In a pure
turbo-jet engine this high temperature would result in a high jet velocity and
consequently lower the propulsive efficiency. However, by using the by-pass
principle, high thermal and propulsive efficiencies can be effectively combined by by-
passing a proportion of the L.P. compressor or fan delivery air to lower the mean jet
temperature and velocity. With advanced technology engines of high by-pass and
overall pressure ratios, a further pronounced improvement in s.f.c. is obtained.
The turbines of pure jet engines are heavy because they deal with the total airflow,
whereas the turbines of by-pass engines deal only with part of the flow; thus the H.P.
compressor, combustion chambers and turbines, can be scaled down. The
increased power per lb. of air at the turbines, to take advantage of their full capacity,
is obtained by the increase in pressure ratio and turbine entry temperature. It is clear
that the by-pass engine is lighter, because not only has the diameter of the high
pressure rotating assemblies been reduced, but the engine is shorter for a given
power output. With a low by-pass ratio engine, the weight reduction compared with a
pure jet engine is in the order of 20 per cent for the same air mass flow.
With a high by-pass ratio engine of the triple-spool configuration, a further significant
improvement in specific weight is obtained. This is derived mainly from advanced
mechanical and aerodynamic design, which in addition to permitting a significant
reduction in the total number of parts, enables rotating assemblies to be more
effectively matched and to work closer to optimum conditions, thus minimising the
number of compressor and turbine stages for a given duty. The use of higher
strength lightweight materials is also a contributory factor.
For a given mass flow, less thrust is produced by the by-pass engine due to the lower
exit velocity. Thus, to obtain the same thrust, the by-pass engine must be scaled to
pass a larger total mass airflow than the pure turbo-jet engine. The weight of the
engine, however, is still less because of the reduced size of the H.P. section of the
engine. Therefore, in addition to the reduced specific fuel consumption, an
improvement in the power-to-weight ratio is obtained.
2.6 SPECIFIC FUEL CONSUMPTION
When comparing engine performance, one of the most important considerations is
how efficiently the power is produced. The amount of fuel consumed to produce a
given horsepower lbs. thrust is known as “specific fuel consumption” or SFC. A
typical aircraft fuel system measures the volume of fuel consumed. This is displayed
in pounds per hour or PPH. To calculate fuel flow, specific fuel consumption found
on the customer data sheet, is multiplied by the horsepower lbs. thrust produced.
2.6.1 SPECIFIC FUEL CONSUMPTION – DEFINITION
SFC = SPECIFIC FUEL CONSUMPTION is defined as the lbs of fuel used per
HP/lbs of thrust per hour.

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2.7 FLAT RATING

“Flat rating” is used by aircraft manufacturers when they select an engine that has a
capability greater than the requirements of the aircraft. They then limit the power
output of the engine. There are three distinct benefits derived from flat rating. One is
the engine will have the ability to make take-off power at lower turbine temperatures
over a wide range of outside air temperatures and pressure altitudes. Performance
at altitude will be greatly enhanced. These two benefits result in the third benefit,
longer engine life. A fourth benefit available on some engines is, a reserve of power
which can be used to boost performance in an emergency ie. Loss of an engine
during take - off.
2.8 PERFORMANCE RATINGS
In the chart, performance ratings are compared on –1 through –12 engines. Notice
the modifiers on the –1, -5, -6, -8 and –10 engines. These temperatures represent
the effects of flat rating engines. Each engine will make take-off power below their
turbine temperature limits to the ambient temperatures indicated. Engines that are
not flat rated, such as the –3 or –11, would be unable to make take-off power below
their turbine temperature limits when operating in conditions above 59°F outside air
temperatures.

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